Real Madrid's Xabi Alonso waves during his official introduction at the Santiago Bernabeu stadium in Madrid on Monday. Photograph: Paul White/AP

If you asked Real Madrid fans to pinpoint when they believed their season might actually turn out to be a success, many would choose the same moment Liverpool fans first thought theirs might not. Two months after Kaká had joined the club, a month after 80,000 fans had packed into the Bernabéu for Cristiano Ronaldo's presentation, Madrid finally met Rafael Benítez's £30m asking price for Xabi Alonso. It was 5 August and, having soared above £250m, Madrid's spending was over at last. They had the team they wanted. Tomorrow night that team has a first opportunity to prove themselves in La Liga against Deportivo La Coruña.

The new Real Madrid will always be defined by Kaká and Ronaldo. In signing the last two winners of the Fifa world player of the year award, Florentino Pérez carried Madrid back to their "rightful place" at the centre of world football, basking in the media spotlight. And yet the signing of Alonso could prove just as significant for the passes he provides and the message his arrival conveys. If Kaká and Ronaldo excited supporters, Alonso allayed their fears; if Pérez's project depends on the stars, coach Manuel Pellegrini's depends on Alonso – the difference between good players and a good team.

Pellegrini spent the summer insisting upon the need to sign the midfielder, telling the media that he "would fit our style perfectly". Alonso wouldn't so much fit Pellegrini's style as impose it; he would provide Madrid's identity. There is a phrase that gets bandied about Spanish football: tell me who your central midfielder is and I'll tell you what kind of team you are. Madrid's central midfielder was Fernando Gago. Or Guti.

"I'm not here to impose order," Alonso insisted. In fact, that's exactly what he's here for. By his own admission, Pellegrini wants him to be the man who "drives" Madrid's play, controlling the "rhythm" of the game. Alongside Lassana Diarra, he also needs to protect the back four. Ronaldo, Karim Benzema and Kaká are not there to defend. "We have to hold our position and provide balance to the team," he explained. "With the attacking players we have got it is very important for us to have a collective spirit. If we can be compact, we will have found a good formula because there's plenty of individual talent. But on your own you're nobody."

It is a message that needed conveying. The coach told Pérez that getting Alonso was "fundamental". The need was all the more pressing for the brilliance of the Barcelona midfield. Pellegrini described him as "unique": no other player on the market could offer the kind of control boasted by Barça's Xavi Hernández.

"The central midfielder is very important because you have to control the pace of the game. You're the player in closest contact with all your team-mates, you're the link between defence and attack," Alonso said. "Pellegrini tells me I am the one that has to offer solutions to the other players; I have to associate myself with them." The more pre-season progressed without him, the clearer it became that Madrid might have great players but there was little pattern, no control. Defending and hitting opponents on the break is fine for most clubs, but Madrid are not most clubs.

But buying Alonso was not just a case of persuading Benítez, it was a case of persuading Pérez. The president was not convinced: he considered Alonso expensive, a man who does not bring in revenue, not worth spending more than £25m on. The fact that he relented was a victory for Pellegrini. It was a victory too for those who demanded that Madrid "Spanishify" the side. Last time Pérez signed just one Spaniard: Sergio Ramos.Much as the departures of Arjen Robben and Wesley Sneijder – two players Pellegrini publicly said he wanted to keep – have reawakened concerns about priorities, the arrival of Alonso was also a sign that this time might be different. Maybe Pérez has learned his lessons – maybe now he will listen to his coach. Alonso does not fit the galáctico mould. Yet he cost more than David Beckham.

"Bit by bit we're adapting and getting to know the coach and what he wants of us," Alonso said, "but we still have to improve lots of things. Slowly we're making steps forward. The challenge now is to make sure that it works like a well-oiled machine." As Madrid approach the first game of a new era, no one expects perfection tonight. It's just a relief to know that, this time, there's someone capable at the controls.